Grasping for an understanding of the true scale of the cosmos is a vital part of how we try to conceptualize reality and our place among it all.
But it's tremendously difficult, whether we're seeking that 'oh wow' moment, or trying to gain intuition that'll help us solve the next scientific problem. So time and time again we look for ways to calibrate our senses, to reach for some kind of perspective.
Perhaps we do this by starting with a thought-experiment about something familiar and cozy.
'Imagine this orange is the Sun'.
Next comes the Earth as a tiny seed, a hundred and nine times smaller, placed about 107 orange-diameters away - that's roughly 320 inches or 9 yards away (I know because I looked up the average diameter of Valencia oranges, really, I did). In this case the outermost major planet, Neptune, is a small blackcurrant located 270 yards further away. The next star, Proxima Centauri, is represented by another orange (actually more like a grape, it's a low mass star) roughly 1,400 miles away.
It's quite effective, we're lured into thinking about something ordinary, and the next thing we know we're gawping at the colossal gulf between us and another sun. You know, one of those thousands of twinkly things you see in the night sky (with good eyesight, in the middle of dark nowhere). It's almost cruel to point out that on this scale the other side of our single galaxy (less than a hundred billionth of the total population of galaxies in the observable universe) would only be reached after traveling about 25 million miles from our citrus mother.
This is one example. Sometimes our Sun is a basketball, or maybe it's the dome of the local planetarium. In fact numerous physical models exist around the world that play this same trick, there's even a list of them on (of course) Wikipedia. A particularly ambitious one is the Sweden Solar System model - stretching literally the length of the country. In this case the Sun (including the corona) is represented by the Ericsson Globe arena in Stockholm.
It's impressive, and by the time you've slogged the nearly 600 miles from the Sun to the termination bow shock above the Arctic circle in northern Sweden, you'll likely appreciate that this is merely a 1:20 million scale representation.
But it's awfully hard to keep all of this in our minds, we're just not used to experiencing such different levels of scale all at once, and a similar challenge exists if we want to go in the other direction, to the microscopic.
These days atoms perhaps don't seem quite as tiny or remote as they once did - even though they typically span barely 0.1 nanometers (a ten-millionth of a centimeter). Ingenious devices like the tiny proboscis of an atomic force microscope can be used to map and even manipulate atoms, as well as sense their covalent bonds with other atoms - all on a run-of-the-mill lab bench.
But once we descend into these structures, the same incredible gulfs in scale separate out their constituents. It's trickier because the physics is trickier, with particles exhibiting their quantum mechanical weirdness, and things get fuzzy. Crudely speaking though, if we scaled the size of something like a gold nucleus to the size of the Sun, the most probable location of the outermost electron of the gold atom would be twice as far away as Pluto's average distance.
It means that similar ratios of space exist inside us to those around us. In fact it's remarkable how much empty space pervades everything we find familiar, and it's one of the reasons the universe can build obscenely dense objects like white dwarfs or neutron stars - there's just a lot of spatial buffer that can be eliminated when you squeeze stuff together.
And of course it doesn't actually stop here. Looking further inwards, it may be (with emphasis on the may), that at a Planck scale (of 10-to-the-power-of-minus-33 centimeters) the fundamental constituents of the universe are resonating strings of compacted, teeny-tiny, multiple dimensions.
Perhaps these are the ultimate granular pieces of nature, but in some ways they're in the middle of nowhere. To try to convey this makes for some even more challenging ratios. For example, first consider that our observable universe stretches in all directions for about 435 billion trillion kilometers, which corresponds to about 4 to-the-power-of-28 centimeters. So the difference in size between the Planck scale and, let's say, a small grape, is roughly equivalent to the difference between that grape and something a 100,000 times larger than the entire observable universe.
But this isn't the full stretch, the full measure of all that there is. The observable universe is merely the universe from which light has had time to propagate to us, from our cosmic horizon. Beyond this? Well, good question. Some theoretical models for a multiverse suggest that there are an infinite number of other universe volumes scattered across these superhorizon scales, so that there are also an infinite number of other universes just like ours, as well as not quite like ours, or entirely unlike ours, and so on.
Of course it might not be that bad. Some of these models, involving what's known as chaotic inflation, suggest that there may be merely 10-to-the-power-of-10-to-the-power-of-10-to-the-power-of-17 other universes. Actually it might not be quite so overwhelming because our paltry human senses would likely only be able to distinguish about 10-to-the-power-of-10-to-the-power-of--16 of these. Why so few you ask? Because the human brain can't assimilate more than about 10-to-the-power-of-16 bits of information, we simply don't have enough atoms in our noggins. I'm sure that makes you feel better.
For me, discussing nature's scales is one of the most challenging, yet thrilling, tasks as a scientist. There is something so wonderful about nature's blatant disregard for us in all of this - and yet here we are.
It's so tremendously important to keep trying though, because perhaps we can get just a handful of those neurons in our brains to see something new. And whenever we see something new we have a chance of understanding ourselves a little bit more.
There is also something just absurdly funny about it all. And of course, as usual, Douglas Adams got there first:
".... Bigger than the biggest thing ever and then some.
Much bigger than that in fact, really amazingly immense, a
totally stunning size, "wow, that's big", time. Infinity is just so
big that by comparison, bigness itself looks really titchy.
Gigantic multiplied by colossal multiplied by staggeringly
huge is the sort of concept we're trying to get across here.”
(D. Adams, The Restaurant At The End Of The Universe)